A combinatorial approach to partitions with parts in the gaps

Volume 85 / 1998

Dennis Eichhorn Acta Arithmetica 85 (1998), 119-133 DOI: 10.4064/aa-85-2-119-133

Abstract

Many links exist between ordinary partitions and partitions with parts in the "gaps". In this paper, we explore combinatorial explanations for some of these links, along with some natural generalizations. In particular, if we let $p^_{k,m}(j,n)$ be the number of partitions of n into j parts where each part is ≡ k (mod m), 1 ≤ k ≤ m, and we let $p*_{k,m}(j,n)$ be the number of partitions of n into j parts where each part is ≡ k (mod m) with parts of size k in the gaps, then $p*_{k,m}(j,n)=p_{k,m}(j,n)$.

Authors

  • Dennis Eichhorn

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